Do bumble bee queens choose nest sites to maximize foraging rate?

Transcription

1 Do bumble bee queens choose nest sites to maximize foraging rate? -Testing models of nest site selection- Yukari Suzuki, Lina G. Kawaguchi, Dulee T. Munidasa, and Yukihiko Toquenaga Division of Integrative Environmental Sciences, Graduate School of Life and Environmental Sciences, University of Tsukuba, JAPAN Complete Affiliation: Division of Integrative Environmental Sciences, Graduate School of Life and Environmental Sciences, University of Tsukuba, 1-1-1, Ten-Nou-Dai, Tsukuba City, Ibaraki , JAPAN Corresponding Author: Yukari Suzuki Tel.: Fax: yukari@m.tains.tohoku.ac.jp Present Affiliation of Corresponding Author: Division of Ecology and Evolutionary Biology, Graduate School of Life Sciences, Tohoku University, Sendai , Japan 27 1

2 Abstract We proposed Foundress-Max hypothesis that a bumble bee foundress chooses her nest site to maximize her energy intake rate from nectar. To examine the hypothesis, we estimated the maximum energy intake rate at each site in the study area, and compared the distribution of the maximum energy intake rates with those of actual nest sites. We also calculated rank correlations of the maximum energy intake rate with the number of nest-searching foundresses at 54 sites. The nest locations supported the Foundress-Max hypothesis, but the number of nest-searching foundresses did not. This could be attributed to the density of food sites: many food sites may attract many foundresses. Therefore, we subsequently proposed Foundress-Sum hypothesis that a foundress chooses her nest site to maximize the sum of energy intake rates. The nest locations supported the Foundress-Max hypothesis more than the Foundress-Sum hypothesis. A profitable food site would affect foundresses nest site selection Keywords: Bombus ardens, net rate of energy intake, nesting site, nest-searching behavior 41 2

3 Introduction Nest location in a given spatial distribution of food resources is an essential factor determining the foraging efficiency in social insects (Dukas and Edelstein-Keshet 1998; Cresswell et al. 2000). In most social insects, a colony occupies a single and immobile nest, and nest mates must go back to their nest after foraging. If the nest is far from food resources, both long traveling times and large energy costs reduce foraging efficiency. Low foraging efficiency will lead to food shortage in nests, which limits their colony development and reproductive success in social insects. In bumble bees, food shortage causes lower blood temperature and torpor in workers (Heinrich 1979), longer development time of immature bees (Plowright and Pendrel 1977; Sutcliffe and Plowright 1988, 1990; Cartar and Dill 1991), and smaller adults (Sutcliffe and Plowright 1990). Colony persistence tended to be low in the meadows where plants that are highly preferred by Bombus were decreased by drought in late season (Bowers 1985). Since decreases in foraging efficiency will limit colony development and persistence, the locations of bumble bee nests should be chosen to maximize foraging efficiency in a given distribution of food resources. Determinants of bumble bee nest locations include foraging efficiency, landscape (e.g., forest boundary or banks), microclimate (i.e., temperature, light, and humidity), and the availability of nest materials. Among these, we considered foraging efficiency to be the most important because it can affect colony development and colony persistence in bumble bees. In our previous study (Suzuki et al. 2007), we proposed a hypothesis that the nest sites are 3

4 chosen so as to maximize the sum of foraging efficiency of workers (Worker-Sum hypothesis). We adopted the net rate of energy intake (Dukas and Edelstein-Keshet 1998; Cresswell et al. 2000) as the foraging efficiency, and constructed a model for calculating the sum of net rates of energy intake at each candidate nest site. Our model indicated that bumble bee nests tended to be located at sites where the sum of energy intake rates in mid season was high. It could be attributed to high colony persistence, and queen s tendency to revisit maternal nest. However, its tendency was weak. Hence, we considered that the foraging efficiency of queens who forage before colony establishment (hereafter foundresses) would be more important than worker s foraging efficiency. Since foundresses choose their nest sites, the net rate of energy intake of a foraging foundress is most likely to affect their nest site selection. Here, we proposed a new hypothesis named the Foundress-Max hypothesis that the nest site is chosen to maximize the net rate of energy intake of a foundress before colony establishment. Based on the Foundress-Max hypothesis, we constructed a new model to calculate the maximum value of the net rates of energy intake. We estimated the maximum energy intake rate at each candidate nest site and found feral nests of Bombus ardens Smith in the study area. To examine this hypothesis, we compared the distribution of the maximum energy intake rates with those of the actual nest sites. In addition, we calculated rank correlations between the maximum energy intake rate and variables of foundresses nest-searching behaviors at 54 sites. We discuss the effect of foraging efficiency on foundress nest site selection, and the application of our model to finding the nest locations of bumble bees and other social insects. 4

5 Model NET RATE OF ENERGY INTAKE We used the net rate of energy intake (Dukas and Edelstein-Keshet 1998; Cresswell et al. 2000) as a foraging efficiency. The net rate of energy intake " (J/s) is expressed as follows: 86 " = (energy from nectar) # (flight cost) (foraging time) + (flight time) (1) We set sugar intake from nectar to be a determinant of energy intake rate. Pollen is also an important floral resource for queens and larvae. It would be ideal to incorporate the net energy intake rate of pollen into our model, but this is difficult to estimate because foragers can get energy from nectar when they collect pollen. The importance of pollen is protein intake that will influence colony success after colony establishment. For calculation of the net rate of energy intake " based on field data, we neglected a cost of flying during foraging: the cost of flying between flowers within a flower patch and the cost of flying between flower patches within a food site. In addition, we assumed a simple foraging process a forager goes straight to a food site, fills its honey stomach at the food site, and returns to the nest (Suzuki et al. 2007). Thanks to this simplification, the calculation of net energy intake rate can be calculated from measurable and relatively few field data (Table 1). The field data were measured in this study (see Materials and Methods). The area was divided into square cells, and the locations of the food and nest sites were defined according to these cells as (i, j) and (x, y), respectively. The energy from nectar is calculated 5

6 as the product of C (µl), S ij (mg/ µl), and E (J/mg) (Table 1). C is the volume of honey stomach. S ij corresponds to the sugar concentration of nectar at the food site (i, j). S ij can be measured in the field. E is the energy gain from sugar. energy from nectar = CS ij E (2) The cost of flying is calculated from M (J/mg/s), W ij (mg), and the flight time. M is a cost of flying per mg of bumble bee s body weight per second. W ij represents the body weight of a foraging bumble bee at the food site (i, j). The flight time is given by D (m) divided by V (m/s). D is twice the Euclidean distance between the food site (i, j) and the nest site (x, y). 109 flight cost = 2W ij M (i " x) 2 + ( j " y) 2 V (3) W ij represents the body weight of a bumble bee with its honey stomach half filled, which approximates the average body weight during the foraging process. According to Comba et al. (1999), the weight of one unit of sucrose solution Ws(N) (mg/µl), where N is sucrose weight per 100 g of solution, can be calculated by Ws(N) = N N (4) We set the body weight of a bumble bee with an empty honey stomach at 200 mg that is an average weight of bumble bees, and the weight of 0.5C µ l of sucrose solution was calculated as 0.5CWs(N). Hence, the body weight becomes W ij = CWs(N ij ). The foraging time is considered as the time to fill the honey stomach, or (CH ij ) /R ij. H ij and R ij can be measured in the field. The sum of the foraging time and the flight time becomes 6

7 120 foraging time + flight time = CH ij + 2 (i " x)2 + ( j " y) 2 R ij V (5) From Eqs. (1), (2), (3), (4) and (5), the net rate of energy intake of a forager that flies to the food site (i, j) from the nest site (x, y) is given by 123 CS ij E # 2W ijm (i # x) 2 + ( j # y) 2 "(x, y,i, j) = V CH ij + 2 (i # x)2 + ( j # y) 2 R ij V (6) 124 The set of " at a candidate nest site (x, y) becomes " x,y = {#(x, y,0,0),#(x, y,1,0), K} MODEL BASED ON THE FOUNDRESS-MAX HYPOTHESIS In spring, bumble bee foundresses wake up from their hibernation and start searching for suitable nest sites. Since a foundress must build her nest and feed her larvae by herself before the emergence of worker adults, she should choose a suitable nest site near a food site where she gets a better net rate of energy intake. Hence, we proposed the Foundress-Max hypothesis that a nest site is chosen to maximize the net rate of energy intake of a foraging foundress before colony establishment. In adopting the Foundress-Max hypothesis, we assumed that a given candidate nest site (x,y) is evaluated according to the maximum value of a set of net rates of energy intake from the candidate nest site, denoted by µ(x, y), in the nest-building season µ(x, y) = max " x,y max.x, max.y " x,y = {#(x, y,i, j) } i= 0, j= 0 (7a) (7b) 137 where " x,y is the set of the net rate of energy intake " from the candidate nest site (x, y) to each 7

8 food site (i, j). We hypothesized that the probability of colony establishment at (x, y) increases as the maximum energy intake rate (µ(x, y) increases. We developed a computer program in C ++ and ran it on a Linux operating system Material and Methods BUMBLE BEES Bombus ardens Smith is commonly observed in meadows, suburbs, and towns in Japan. At the end of March, foundresses wake up from their hibernation and search for nest sites. Nests are often established inside the abandoned burrows of rodents, in cavities between rocks and soil, or in gaps between artificial structures. From mid April to early June, workers emerge and forage for floral resources. If the colony grows sufficiently, it produces gynes and males from mid to late June, and then the colony collapses gradually until the end of June STUDY AREA We collected field data in Kasama, Ibaraki Prefecture Japan (N 36 22', E '). The landscape consists of residential areas, parks, paddy fields, woodland, and a mountain. The study area was set to an area of 2.5 km " 2.5 km. We recorded locations where B. ardens queens were foraging as food sites on a map. Spatial scale of a food site varied from 1 plant (e.g. a tree of Rhododendron sp.) to a patch of dozens of plants (e.g. a bush of Rubus palmatus). If patches of different plant species were spatially overlapped (though such cases were rare), and both were visited by B. ardens, 8

9 we recorded both species on the map. We divided the study area into 100 "100 cells, and projected the points of food sites for each cell (25 m " 25 m) ESTIMATION OF NET ENERGY INTAKE RATE We estimated standing crop R ij, sugar concentration of nectar S ij, and foraging time per flower H ij used in the equation of the net rate of energy intake from field data. The field study of these R ij, S ij, and H ij was conducted from 8th 29th April In our study area, different plant species flowered one after another in April. If foundresses made decision on their nest-site selection for a short time, the accuracy of model estimation would be affected by the seasonal change of the flowering plants. To track the seasonal change of the flowering plants, we divided one month into three periods, and measured standing crop ( R) and sugar concentration ( S) of nectar, and foraging time per flower ( H) for each flower species in each period. At food sites where B. ardens was foraging, nectar was drawn from flowers with glass microcapillaries (Drummond Microcaps, Drummond Scientific Co., Broomall, PA, capacity: 0.2, 0.5, 1, 2, 3, 5, 10 µl), and its volume ( R µl) was calculated from the length of the fluid column. Then, its sugar concentration of drawn nectar was measured as N (g per 100 g of sucrose solution) with a handheld refractometer (Eclipse; Bellingham and Stanley Ltd., Tunbridge Wells, UK). N (g per 100 g ) was converted to S (mg per 1µl). We also measured the foraging time of B. ardens over 5 to 48 consecutive flower visits. Foraging time per flower ( H) was averaged for observations of 1 5 foundresses (8 to 122 total flower visits). We excluded the effect of pollen from our evaluation by investigating bumble 9

10 bee foragers that carry no pollen. We obtained H (sec) as the ratio of the measured foraging time divided by the number of flowers visited. Standing crop of nectar ( R) and its sugar concentration ( S) were averaged for 5 to 17 flowers of each plant species. We obtained the parameter sets ( R, S and H) for five plant species in total. Using R ij, S ij, and H ij measured in the field, we calculated the net rate of energy intake for each period in the study area TESTS OF HYPOTHESES Comparison of the distribution of the maximum energy intake rate ( µ(x, y)) with those at four nest sites The nest search was independent of model prediction. We searched the study area for nests, and found bumble bees by eyes during the nest search in April and May. We usually did not follow the foundresses from the food sites to exclude a sampling bias. We tried to find all nests in the study area, but it is possible that we failed to find some nests because finding feral nests was difficult. We found six natural B. ardens nests (colonies I-VI) in the study area in April. Colony I was located at site A, and colonies II and III were located in the same cell, at site B. Colonies IV and V were located at site C, and colony VI was located at site D (Fig. 1). We compared the distribution of the maximum energy intake rate (µ(x, y)) with those of the actual nest sites. We assumed that actual nest sites supported the hypothesis if µ(x, y) at actual nest sites were included within the upper 5% of the µ(x, y) distribution. Since the rank of µ(x, y) did not include the number of the cells with the same µ(x, y), we defined a hot zone area" as the 10

11 number of cells with µ(x, y) that was equal to or higher than µ(x, y) of the cell for the nest site. Then, the hot zone area of the nest site was less than 500 (i.e. 5% of all cells) if µ(x, y) at the nest site were included within the upper 5% of the µ(x, y) distribution. We calculated the hot zone area of each actual nest site using the net rate of energy intake of a foraging foundress in early, mid, and late April Rank correlation between the average of the maximum energy intake rates and foundress nest-searching behaviors Although we searched a large area for nests, our nest-searching efforts might be biased toward the area close to food sites or where nests of B. ardens were previously found. To exclude possible biases of sampling efforts, we investigated nest-searching behavior of foundresses in quadrats selected almost randomly. We selected 54 cells, and set a quadrat as a square area (25 " 25 m) on the location of each selected cell in the study area. Then, we made a preliminary examination of whether we could conduct our census in the candidate cells in the study area. If we could not conduct our census in the candidate cells due to its geographical feature (e.g. steep slope) or landownership, we set an alternative quadrat nearby. About 10% of the study area is unsuitable to follow nest-searching foundresses due to its geographical feature though we could search for food sites in the area. About 30% of the study area is residential area. 11

12 Observation of foundresses was carried out on 6, 9, 13, 14, and 17 April Observation time was 9:00-10:30 a.m. (first period) and 11:00 a.m. - 12:30 p.m. (second period). Each observer randomly walked searching for bumble bee foundresses about for 90 minutes in the quadrat. Once detected, a foundress was observed continuously until it flew away from the quadrat. We measured (i) the total number of observed foundresses. Observed foundresses were searching for suitable nest sites (flying in a zigzag pattern close to the ground and occasionally landing on and investigating the ground surface), resting on the ground or vegetation, just passing through, or foraging in the quadrat. To exclude the possible correlation between the number of foraging foundresses and the availability of food resources, we also measured (ii) the number of nest-searching foundresses. To evaluate a queen s eagerness to search for nest site in focal quadrat, we also measured (iii) the time spent on the nest-searching behavior. We calculated the rank correlation between the average of the maximum energy intake rates in early and mid April (µ(x, y)) and each variable of the foundress nest-searching behaviors. Kendall s tau with blocking variables (Korn 1984) was calculated for each combination, and conditional independence was tested. In this study, observation period (first/second) was treated as a blocking variable Results 1: Tests of the Foundress-Max hypothesis COMPARISON OF THE DISTRIBUTION OF THE MAXIMUM ENERGY INTAKE RATE ( µ(x, y)) 236 WITH ACTUAL NEST LOCATIONS 12

13 The Foundress-Max hypothesis was supported by the actual nest locations. The maximum energy intake rate ( µ(x, y)) predicted all actual nest sites using the net rate of energy intake of a foraging foundress in early April (Fig. 1). The hot zone areas of four actual nest sites in early April were less than 500, or 5% of all cells (Table 2). Except for site D, the hot zone areas of the actual nest sites in mid April were also less than 5% of all cells. The hot zone areas of the actual nest sites where there were two colonies (sites B and C) were smaller than those where there was one colony (sites A and D). We also calculated the hot zone areas for the actual nest locations based on the Worker-Sum hypothesis that we proposed in our previous study (Suzuki et al. 2007). The Worker-Sum hypothesis was not supported by the actual nest locations in this study (Table A1 in Appendix A) RANK CORRELATION BETWEEN THE AVERAGE OF THE MAXIMUM ENERGY INTAKE RATES (µ(x, y)) AND FOUNDRESS NEST-SEARCHING BEHAVIORS 79 out of 132 observed foundresses showed nest-searching behavior, whereas only 13 foundresses were foraging in the quadrats. Although the average of the maximum energy intake rates (µ(x, y)) was positively correlated with the number of nest-searching foundresses, the Foundress-Max hypothesis was not supported by the foundress nest-searching behaviors. When observation period was treated as a blocking variable, the positive rank correlations between µ(x, y) and the three variables of the foundress nest-searching behavior were not significant (the total number of 13

14 foundresses: blocked " = , P = ; the number of nest-searching foundresses: blocked " = , P = ; time spent on nest searching behavior: blocked " = , P = ) Alternative hypothesis If the Foundress-Max hypothesis were plausible, the average of the maximum energy intake rates ( µ(x, y)) and nest-searching behaviors would significantly correlate. However, rank correlation with nest-searching behaviors did not support the Foundress-Max hypothesis. We considered that this might be attributed to the density of food sites. When the density of food sites becomes high, the search areas of various foundresses overlap (Fig. 2). As the number of nest-searching foundresses increases, the probability of colony establishment also increases if the availability of nest sites is not limiting. Hence, we considered an alternative hypothesis: the Foundress-Sum hypothesis that a nest site may be chosen to maximize the sum of the net rates of energy intake of a foraging foundress before colony establishment. In adopting the Foundress-Sum hypothesis, we assumed that a given candidate nest site (x,y) is evaluated according to the sum of net rates of energy intake of a foraging foundress from the candidate nest site, denoted by "(x, y), before the nest-building season. max. x max. y "(x, y) = $ $ #(x, y,i, j) (8) i j 14

15 We had hypothesized that the probability of colony establishment at (x, y) increases as the sum of energy intake rates ( "(x, y) increases. We calculated the hot zone area based on the Foundress-Sum hypothesis using the net rate of energy intake of a foraging foundress in early, mid, and late April. We also calculated the rank correlations between the average of the sum of energy intake rates in early and mid April ("(x, y)) based on the Foundress-Sum hypothesis and each variable of foundress nest-searching behaviors in the 54 quadrats Results 2: Tests of the Foundress-Sum hypothesis COMPARISON OF THE DISTRIBUTION OF THE SUM OF ENERGY INTAKE RATES ("(x, y)) 285 WITH ACTUAL NEST LOCATIONS The Foundress-Sum hypothesis was partially supported by the actual nest locations. Hot zone areas for two actual nest sites were less than 5% of all cells in the case of using the net rate of energy intake of a foraging foundress in early and mid April (Table 3). Although the Foundress-Max hypothesis was supported by more actual nest sites than the Foundress-Sum hypothesis, the hot zone areas based on the Foundress-Sum hypothesis were smaller than those based on the Foundress-Max hypothesis at site B in early April, and at site C in mid April (Tables 2 and 3) RANK CORRELATION BETWEEN THE AVERAGE OF THE SUM OF ENERGY INTAKE RATES ("(x, y)) AND FOUNDRESS NEST-SEARCHING BEHAVIORS The Foundress-Sum hypothesis was supported by the foundress nest-searching behaviors. The 15

16 positive rank correlation between the average of the sums of energy intake rates based on the Foundress-Sum hypothesis ("(x, y) and the total number of foundresses was significant (blocked " = , P = ; the number of nest-searching foundresses: blocked " = , P = ; time spent on nest searching behavior: blocked " = , P = ). When the data collected at different observation periods were analyzed separately, the positive correlation between "(x, y) and the total number of foundresses, and the positive correlation between "(x, y) and the number of nest-searching foundresses in the first period also became significant (Fig. 3) Discussion Here we proposed two hypotheses: Foundress-Max and Foundress-Sum. In the Foundress-Max hypothesis, nest site is chosen to maximize the net rate of energy intake of a foraging foundress before colony establishment. In the Foundress-Sum hypothesis, nest site is chosen to maximize the sum of net rates of energy intakes of a foraging foundress before colony establishment. Through field investigation, we estimated the maximum energy intake rate (µ(x, y)) and the sum of energy intake rates ("(x, y)) at each site in the study area. We found six feral nests at four nest sites, and investigated foundress nest-searching behaviors at 54 quadrats in the study area. To examine the hypotheses, we compared the µ(x, y) distribution or the "(x, y) distribution with those of the actual nest sites, and the rank correlation with foundress nest-searching behavior. The Foundress-Max hypothesis was supported by the actual nest locations (Fig. 1). The maximum energy intake rates (µ(x, y)) at four actual nest sites were included within upper 5% of 16

17 the µ(x, y) distribution in early April, and µ(x, y) at three actual nest sites were included within upper 5% of the µ(x, y) distribution in mid April (Table 2). The Foundress-Sum hypothesis was partially supported by the actual nest locations. The sums of energy intake rates ("(x, y)) at two actual nest sites were included within upper 5% of the "(x, y) distribution in early and mid April (Table 3). In addition, the number of nest-searching foundresses in the morning was significantly correlated with "(x, y) in early and mid April (Fig. 3). This result suggests that foundresses need more energy to maintain their body temperature during the relatively colder morning period. During field observation, foundresses seemed to search areas far from food sites in the afternoon. They sometimes tried to build their nests in the sites far from food resources, but abandoned the incomplete nests after several days (Y. Toquenaga, personal communication). This may be attributed to low net rates of energy intake. On the other hand, the Worker-Sum hypothesis proposed in our previous study (Suzuki et al. 2007) was not supported here (Appendix A and Table A1). Based on these results, we concluded that a bumble bee foundress chooses her nest sites to maximize her net rate of energy intake before colony establishment. However, our results raised two questions: First, what factors contributed to the higher accuracy of the maximum energy intake rate (µ(x, y)) based on the Foundress-Max hypothesis than of the sum of energy intake rates ("(x, y)) based on the Foundress-Sum hypothesis in predicting the actual nest locations? The nests were located at sites with higher µ(x, y), but the number of nest-searching foundresses in the morning was significantly correlated with "(x, y). Second, why was the Worker-Sum hypothesis 17

18 not supported in this study? In our previous study (Suzuki et al. 2007), we had proposed the Worker-Sum hypothesis that nest site is located to maximize the sum of net rates of energy intake of a foraging worker after colony establishment. When we calculated the sum of energy intake rates ( I(x, y) based on the Worker-Sum hypothesis at the actual nest sites, the sum of I(x, y) at the actual nest sites was significantly higher than that of sites selected randomly in the case of using the net rate of energy intake of a foraging worker in mid May. However, in this study, the sum of I(x, y) at the actual nest sites was not significantly higher than that of sites selected randomly. In the following two subsections, we discuss these two questions. In addition, we propose an application of our model to finding the nests of central-place foragers in the last subsection NEST LOCATIONS AND NEST-SEARCHING FOUNDRESSES The maximum energy intake rate (µ(x, y)) based on the Foundress-Max hypothesis was more accurate for predicting the actual nest locations than the sum of energy intake rates ("(x, y)) based on the Foundress-Sum hypothesis. In the Foundress-Max hypothesis, an area with high µ(x, y) means an estimated nest area that does not take nest density into account. In the Foundress-Sum hypothesis, an area with high "(x, y) means an estimated area with high foundress density and high nest density, which results in low "(x, y) with low nest density. Hence, "(x, y) was effective for predicting the density of foundresses whereas µ(x, y) was effective for predicting nest locations regardless of nest density. In addition, competition among foundresses may have affected the probability of colony 18

19 establishment. A high foundress density may lead to competition for floral resources and nest sites. Since foundresses compete for nest sites and sometimes fight to the death, the probability of colony establishment would not simply be proportional to the number of nest-searching foundresses. This phenomenon may appear in other animals whose foraging patterns are central-place foraging because competition for nest sites has been reported in various species, especially in birds (e.g., Renton 2004) COLONY PERSISTENCE AND REPRODUCTIVE SUCCESS In our previous study (Suzuki et al. 2007), the Worker-Sum hypothesis was weakly supported by actual nest locations. We had proposed two possible reasons why the sum of the net rates of energy intake of a foraging worker affected colony presence. First, foundresses may choose nest sites based on the food availability before colony establishment, but colonies will go extinct at poor sites after colony establishment. If the first reason is correct, µ(x, y) based on the Foundress-Max hypothesis or "(x, y) based on the Foundress-Sum hypothesis could estimate the nest site selection by foundresses, and I(x, y) based on the Worker-Sum hypothesis could estimate colony persistence. Second, foundresses select nest sites where food availability will increase after colony establishment by revisiting maternal nest sites. If the second reason is correct, I(x, y) based on the Worker-Sum hypothesis could estimate the nest site selection by foundresses. In this study, µ(x, y) and "(x, y) led to the successful prediction of actual nest sites. This seems to support the first explanation as stated above. However, we did not observe colony 19

20 extinction, and I(x, y) were low at actual nest sites in Moreover, colony development seems to be independent of I(x, y), because the colony development and the reproductive success of two colonies at the same site were varied (Table B1 in Appendix B). This result may be attributed to the other factors before colony establishment, e.g., length of the foundress hibernation (Beekman and van Stratum 2000). Since the positive effects of food availability on colony development and persistence have been discussed in many previous studies in bumble bees (Heinrich 1979; Plowright and Pendrel 1977; Bowers 1985; Sutcliffe and Plowright 1988, 1990; Cartar and Dill 1991; Schmid-Hempel and Schmid-Hempel 1998) and other bees (e.g., Williams and Kremen 2007), we must further examine the effect of the net energy intake rate on colony development, colony persistence and reproductive success in future studies APPLICATION TO FINDING NEST LOCATIONS Bumble bee foraging behavior has been studied in many experiments using commercial colonies (e.g., Osborne et al. 1999; Worden and Papaj 2005; Burns and Thomson 2006), but the ecology of wild bumble bees remains largely unclarified due to the difficulty of finding their nests. In this study, the hot zone area also represents the total area that must be searched to find a nest based on the maximum energy intake rate or the sum of energy intake rates. If we could develop a method to estimate bumble bee nest locations based on our model, it would be a useful tool for future studies. Since bumble bees are major pollinators of numerous plants, the estimation of nest locations would be also useful in pollination ecology and plant conservation ecology. 20

21 Bumble bees nest locations can be affected by foraging efficiency, landscape, microclimate, and the availability of nest materials. As well as nectar, pollen is an important floral resource for queens and larvae. If a foundress chooses her nest site to maximize her fecundity and larvae s growth rate at the beginning of colony establishment, the protein intake of pollen should also affects nest locations. Landscape affects the nest site selection by bumble bee foundresses (Svensson et al. 2000; Kells and Goulson 2003), and microclimate is frequently correlated with landscape (Kells and Goulson 2003). The availability of nest materials may also be correlated with landscape. Our model can predict the nest locations of B. ardens because B. ardens is opportunistic species that is not severely restricted by specific nest materials. However, species that build nests underground (e.g., B. diversus, B. hypocrita) would need specific nest materials. If landscape can be incorporated into our model, the accuracy of prediction may increase for the case of species that need specific nest materials. Lonsdorf et al. (2009) proposed a model of pollinator abundance on a landscape using high-resolution (1m) aerial photographs and GIS. Integration with landscape information using GIS will be necessary for application to finding nest locations. However, we have only a relatively large mesh landscape information (100m "100m) in the study area whereas cell size in our model was small (25m " 25m). We will have to test whether the landscape information in this scale can represent the spatial heterogeneity of specific nest materials. Further studies are needed to clarify whether our model can be applied to estimate nest locations of the same species in different areas, to estimate nest locations of different bumble bee species, and to estimate nest locations of different species whose foraging pattern is central-place 21

22 416 foraging Acknowledgements We thank Kazuharu Ohashi, Teruyoshi Nagamitsu, and Yoh Iwasa for their helpful advice. We also thank Maki Inoue for her fruitful input. Yoshiko Shimono, Takashi T. Makino, Hiroyuki Mano, Chikako Ishida, Takumi Komuro, and Tomonori Yanaka helped us to search for the nests of bumble bees and investigate the nest-searching behaviors of foundresses. This experiment was conducted in compliance with current laws in Japan References Allen, T., Cameron, S., McGinley, R., and Heinrich B. (1978) The role of workers and new queens in the ergonomics of a bumblebee colony (Hymenoptera: Apoidea). Journal of the Kansas Entomological Society 51, Beekman, M. and van Stratum, P. (2000) Does the diapause experience of bumblebee queens Bombus terrestris affect colony characteristics? Ecological Entomology 25, 1-6. Bowers, M.A. (1985) Bumble bee colonization, extinction, and reproduction in subalpine meadows in Northeastern Utah. Ecology 66, Burns, J.G. and Thomson, J.D. (2006) A test of spatial memory and movement patterns of bumblebees at multiple spatial and temporal scales. Behavioral Ecology 17, Cartar, R.V. and Dill, L.M. (1991) Costs of energy shortfall for bumble bee colonies: predation, 22

23 social parasitism, and brood development. Canadian Entomologist 123, Comba, L., Corbet, S.A., Barron, A., Bird, A., Collinge, S., Miyazaki, N. and Powell, M. (1999) Garden flowers: Insect visits and the floral reward of horticulturally-modified variants. Annals of Botany 83, Cresswell, J.E., Osborne, J.L. and Goulson, D. (2000) An economic model of the limits to foraging range in central place foragers with numerical solutions for bumblebees. Ecological Entomology 25, Dukas, R. and Edelstein-Keshet, L. (1998) The spatial distribution of colonial food provisioners. Journal of Theoretical Biology 190, Ellington, C.P., Machin, K.E. and Casey, T.M. (1990) Oxygen consumption of bumblebees in forward flight. Nature 347, Heinrich, B. (1979) Bumblebee Economics. Harvard University Press, Cambridge. Kells, A.R. and Goulson, D. (2003) Preferred nesting sites of bumblebee queens (Hymenoptera: Apidae) in agroecosystems in the UK. Biological Conservation 109, Korn, E.L. (1984) Kendall-tau with a blocking variable. Biometrics 40, Lonsdorf, E., Kremen, C., Ricketts, T., Winfree, R., Williams, N., and Greenleaf, S. (2009) Modelling pollination services across agricultural landscapes. Annals of Botany doi: /aob/mcp069 Osborne J.L., Clark, S.J., Morris, R.J., Williams, I.H., Riley, J.R., Smith, A.D., Reynolds, D.R. and Edwards, A.S. (1999) A landscape-scale study of bumble bee foraging range and constancy, using 23

24 harmonic radar. Journal of Applied Ecology. 36, Plowright, R. C. and Pendrel, B. A. (1977) Larval growth in bumble bees (Hymenoptera: Apidae). Canadian Entomologist 109, Renton, K. (2004) Agonistic interactions of nesting and nonbreeding Macaws. The Condor 106, Schmid-Hempel, R. and Schmid-Hempel, P. (1998) Colony performance and immunocompetence of a social insect, Bombus terrestris, in poor and variable environments. Functional Ecology 12, Sutcliffe, G. H. and Plowright, R. C. (1988) The effects of food supply on adult size in the bumble bee Bombus terricola Kirby (Hymenoptera: Apidae). Canadian Entomologist 120, Sutcliffe, G. H. and Plowright, R. C. (1990) The effects of pollen availability on development time in the bumble bee Bombus terricola K. (Hymenoptera: Apidae). Canadian Journal of Zoology 68, Suzuki, Y., Kawaguchi, L.G. and Toquenaga, Y. (2007) Estimating nest locations of bumblebee Bombus ardens from flower quality and distribution. Ecological Research 22, Svensson, B., Lagerlöf, J., and Svensson, B.G. (2000) Habitat preferences of nest-seeking bumble bees (Hymenoptera: Apidae) in an agricultural landscape. Agriculture, Ecosystems and Environment 77, Williams, N.M. and Kremen, C. (2007) Resource distributions among habitats determine solitary bee offspring production in a mosaic landscape. Ecological Applications 17,

25 Worden B.D. and Papaj, D.R. (2005) Flower choice copying in bumblebees. Biology Letters 1,

26 78 Appendix A: Worker-Sum hypothesis 79 In our previous study, we had proposed the Worker-Sum hypothesis that nest site is located to maximize 80 the sum of net rates of energy intake of a foraging worker after colony establishment (Suzuki et al ). In adopting the Worker-Sum hypothesis, we had assumed that a given candidate nest site (x, y) 82 is evaluated according to the sum of net rates of energy intake of a foraging worker from the candidate 83 nest site, denoted by I(x, y), after the nest-building season. The equation of I(x, y) is the same as Eq. 84 (8) in the Foundress-Sum hypothesis, however, the net rate of energy intake of a foraging worker after 85 colony establishment is used in the equation of I(x, y). We had hypothesized that the probability of 86 colony establishment at (x, y) increases as the evaluation value I(x, y) increases. 87 The Worker-Sum hypothesis was not supported in this study. I(x, y) predicted no actual nest 88 sites in May and June (Table A1). In Suzuki et al. (2007), the sum of I(x, y) at the actual nest sites 89 using the net rate of energy intake of a foraging worker in mid May was significantly higher than that of 90 sites sampled randomly in a randomization test. However, the sum of I(x, y) at actual nest sites was not 91 significantly higher than those of sites sampled randomly in this study (e.g., P= in mid May) Appendix B: Measurement of colony development

27 94 We dug out colonies II and III from site B, and colonies IV and V from site C after maturation of 95 sexuals in colonies. The physical size of each nest and the total number of cocoons were measured as the 96 indicators of colony development. Large cocoons were also counted because they can be considered as 97 cocoons of sexuals. Cocoons having a width greater than 10 mm were regarded as large cocoons. 98

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